I agree with Doug - assuming you don't have errors in the referenced ranges it looks like #VALUE! error would only be caused by trying to apply a ROUND
function to a text value - this version should avoid that error
=IF(J5="YES",SUM(IF(E10:I610>11538,IF(E10:I610<=34760,IF(A10:A610="No",ROUND(E10:I610*0.056,0)),IF(ISNUMBER(E10:I610),ROUND(34760*0.056,0))))),0)
confirmed with CTRL+SHIFT+ENTER
.....but check the result because the fix might effect the expected result
Note: if E10:I610 is > 34760 then the sum includes 34760*0.056 rounded (i.e. 1947) regardless of the column A value (as per your formula). Is that the intent?
Re your comment - this revised version should do what you want
=IF(J5="YES",SUM(IF(E10:I610>11538,IF(A10:A610="No",IF(ISNUMBER(E10:I610),ROUND(IF(E10:I610>34760,34760,E10:I610)*0.056,0))))),0)